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Antiderivatives: MATH 171 Problems 4-6 thumbnail

Antiderivatives: MATH 171 Problems 4-6

Proving facts about antiderivatives and a physics application

AccelerationAntiderivativeAntiderivative of a FunctionDerivativeIndefinite IntegralInitial ConditionIntegralPositionVelocity
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Definite Integrals: MATH 171 Problems 5-9 thumbnail

Definite Integrals: MATH 171 Problems 5-9

The definition and properties of definite integrals

Area under a curveCircleDefinite IntegralIntegralLimitNorm of a PartitionPartition of an IntervalPolynomialRadiusRiemann SumRight EndpointsSquare Root
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Fundamental Theorem of Calculus: MATH 171 Problems 1-3 thumbnail

Fundamental Theorem of Calculus: MATH 171 Problems 1-3

Proving and then applying the Fundamental Theorem of Calculus

AntiderivativeAntiderivative of a FunctionConcave DownConcave UpContinuousDerivativeDifference QuotientDifferentiableExtreme Value TheoremFundamental Theorem of CalculusGraphGraph of AntiderivativeGraph of DerivativeIncreasingIntegralLimitSqueeze (or Sandwich) Theorem
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Integration by Substitution: MATH 171 Problems 4-6 thumbnail

Integration by Substitution: MATH 171 Problems 4-6

Using u substitution to evaluate integrals and prove facts about logarithms and integrals and

CosineDefinite IntegralIndefinite IntegralIntegralLogarithmSineTrigonometryu substitution
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Definite Integrals: MATH 172 Review thumbnail

Definite Integrals: MATH 172 Review

Review of the definition of a definite integral

Area under a curveDefinite IntegralDefinite Integral RulesIntegrable FunctionIntegral RulesLimits of IntegrationPartition of an IntervalRiemann Sum
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Fundamental Theorem of Calculus and u-Substitution: MATH 172 Problems 4-7 thumbnail

Fundamental Theorem of Calculus and u-Substitution: MATH 172 Problems 4-7

Proving the Fundamental Theorem of Calculus and examples of u Substitution

Even FunctionFundamental Theorem of CalculusIndefinite IntegralIntegrable FunctionSecantTangentu substitution
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Integral and Comparison Tests: MATH 172 Problems 4-7 thumbnail

Integral and Comparison Tests: MATH 172 Problems 4-7

Proving the Integral, Comparison, and Limit Comparison Tests

Comparison TestConvergent SeriesDivergent SeriesIntegral TestLimit Comparison TestMonotone Sequence TheoremPartial Sum of SeriesPartition of an IntervalRiemann Sum
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Power Series: MATH 172 Problems 1-3 thumbnail

Power Series: MATH 172 Problems 1-3

Covering Radius and Interval of Convergence of Power Series

Absolute ConvergenceAlternating Series TestComparison TestDivergence TestDivergent SeriesGeometric SeriesIntegral TestLimitp SeriesPower SeriesPower Series Convergence
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Power Series as Functions: MATH 172 Problems 4 & 5 thumbnail

Power Series as Functions: MATH 172 Problems 4 & 5

Examples about the derivative and integral of a power series

Derivative of a Power SeriesDifferential EquationPower SeriesPower Series ConvergenceRadius of ConvergenceRatio Test
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